Dynamic Interactions of Stock Market and Foreign Exchange ... · market and foreign exchange market...

Dynamic Interactions of Stock Market and Foreign Exchange Market

for Six OECD Countries during the US Financial Crisis

by

Hong-Ghi Min1*, Sang-Ook Shin1 and Yonghwan Jo1

This Draft: 17 January 2013

1 Department of Management Science, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701

*Correspondence. E-mail: [email protected], Tel: +82-42-350-6305

2

Dynamic Interactions of Stock Market and Foreign Exchange Market

for Six OECD Countries during the US Financial Crisis

Abstract

We investigate the dynamic relationship between stock returns and exchange rate changes for six OECD countries during and after the US financial crisis period. First, dynamic conditional correlations (DCCs) estimated from the DCC-GARCH model show negative DCCs (substitution effect) for stock returns and exchange rates changes in US and Japan while model provides positive DCCs (wealth effect) for stock returns and exchange rate changes in United Kingdom, Australia, and Canada for the sample period.

Second, DCCs for stock returns and exchange rates changes increase for all six countries (US and Japan: in absolute value) after the Lehman failure and remain high during the post-crisis adjustment period, i.e., dynamic link between two markets become stronger after the US financial crisis.

Third, using Bai-Perron test and Markov-Switching model, we investigate changing patterns of causality for different phases of crisis periods and it is shown that exchange rate changes cause stock return changes during the contagion period of the crisis in Australia, Canada, Japan, Switzerland and US, i.e., when volatility of (stock returns and) exchange rate changes are very high, exchange rate changes lead stock return changes. However, UK does not show any causal relationship at all.

Finally, it is shown that VIX index and TED spread increase conditional correlations between stock returns and exchange rate changes while CDS spread decrease conditional correlations.

Key words: GARCH, dynamic conditional correlation, wealth effect, substitution effect,

Market-Switching causality test, VIX index, TED spread, CDS spread

JEL classification code:

3

I. Introduction

On September 15, 2008, Lehman Brothers Holdings, 4th largest investment bank in

the US, declared bankruptcy. After two weeks, the Standard & Poor’s 500 index plunged

106.85 points or 8.81%. The Lehman’s failure becomes the symbol of the subprime mortgage

crisis happened in 2008, which created unexpectedly huge shocks in global economy.

Because the shocks caused fundamental changes in both stock market and foreign exchange

market during the crisis, it is essential to understand the dynamic relationships between stock

market and foreign exchange market during the crisis.

Many studies have reviewed the dynamic interactions between stock market and

foreign exchange market in theoretical and/or empirical approaches. According to traditional

“Flow approach” (Dornbush and Fisher:1980), on the one hand, the changes in domestic

currency value may affect relative competiveness of export goods in international market,

thereby increasing stock prices, i.e., change in exchange rates causes change in stock prices.

On the other hand, stock price returns may give rise to change in domestic money demand

through substitution effect or wealth effect, thereby affecting the value of domestic currency,

i.e., change in stock prices leads change in exchange rates [Friedman (1988), Gavin (1989),

and Choudhry (1996)]. “Portfolio-balance” or “Stock approach” [Branson (1983), Branson

and Henderson (1985), and Frankel (1983)] claims that increase in domestic stock prices

causes local currency appreciation since investors rebalance their portfolio. In this model,

changes in stock prices cause appreciation of domestic currency.

To investigate the dynamic interactions between stock market and foreign exchange

market, this paper focuses on the following research questions. First of all, we find phases of

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time varying correlations between stock market and foreign exchange market. While the

advantages of GARCH-type model allow researchers to measure volatility in financial

markets, the method of dynamic conditional correlations (Engle, 2002) enables time varying

analysis between stock market and foreign exchange market. In this question, we derive

dynamic conditional correlations (DCCs) for 6 OECD countries to find different phases of

DCCs during the financial crisis. Whereas a number of previous studies adopt uniform phases

for whole countries that are derived arbitrarily by researchers, we identify the phases by

estimating unknown structural breaks of Bai and Perron (2003).

In addition, we also investigate changes in causal relationships between two markets.

Using structural breaks derived from the Bai-Perron tests, we initiate the Granger causality

test if stock market returns cause exchange rate changes for different phases of financial crisis

spillover period. From the Granger causality test, we find that lead of exchange market to

stock market becomes dominant during the crisis period in all countries, except UK. To figure

out why causalities are changing over different phases of financial crisis, we use regime-

switching causality test and it is shown that exchange rate changes lead stock returns when

volatility of foreign exchange market is high.

Finally, to find transmission channels of two financial markets, we use dynamic

conditional correlation with exogenous variables (DCCX) model of Min and Hwang (2011)

and we find that exogenous variables, such as the implied volatility of S&P 500 index options

(VIX), the implied volatility of foreign exchange rate between US dollar and Euro (FXV), the

international interest difference of each country over LIBOR (TED), and CDS spread of each

country (CDS), to determine the time varying correlations between stock market and foreign

exchange market.

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This paper is organized as follows. In Section 2, we review previous literatures about

the interactions between stock market and foreign exchange market. Section 3 introduces

DCC-MGARCH model and estimates DCCs for 6 OECD countries. Section 4 provides

different phases in DCCs using the Bai-Perron tests and investigates changes in Granger-

causality by using sub-samples from multiple structural breaks and Markov process. In

Section 5, we analysis determinants of DCC in the DCCX model and the final section

conclude this paper.

II. Literature Reviews

Studies on dynamic interactions of stock market and foreign exchange market can be

classified into three different groups.

First group of studies try to evaluate the exchange rate exposure of multinational

firms by testing ICAPM (International CAPM). Jorion (1991) examines the pricing of

exchange rate risk in the US stock market, using two factor and multi-factor arbitrage pricing

models. The evidence is presented that the relation between stock returns and the value of the

dollar differs systematically across industries. Dumas and Solnik (1995) investigates whether

exchange rate risks are priced in international asset markets using a conditional approach that

allows for time variation in the rewards for exchange rate risk. The results for equities and

currencies of the world's four largest equity markets support the existence of foreign

exchange risk premium. Choi et al. (1998), using an unconditional and a conditional multi-

factor asset pricing model, investigate whether exchange risk is recognized and priced in

Japan and find that exchange risk is generally well-priced in Japan. They provide evidence, in

the unconditional model, that the exchange risk is priced in both weak and strong yen periods

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when yen-US dollar exchange rate is used. Muller and Verchoor (2009), motivated by Bartov

et al. (1996), investigate the impact of increased exchange rate variability on the stock return

volatility of US multinationals by focusing on the turmoil periods around the major financial

crises of the last decade: Mexico’s float of the peso in December 1994, Argentina’s financial

crisis and its efforts not to devalue the Argentine peso in March 1995. By using a sample of

673 US-multinational firms with real operations in the crisis-contaminated countries, they

find that the stock return volatility of US multinational firms increases significantly in the

aftermath of a financial crisis, even relative to the increase in stock return volatility for other

US firms belonging to the same industry sector and market capitalization class that are not

active in the crisis countries.

Second group of studies focuses on the asymmetric interactions of two market using

exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model.

Kanas (2000) investigates the relationship between stock returns and exchange rate changes

using EGARCH model for the six industrialized countries. He finds (i) the evidence of

spillovers from stock returns to exchange rate changes for all countries except Germany, (ii)

spillovers from stock market to exchange market are symmetric; the effect of ‘bad’ news is

indifferent with that of ‘good’ news and (iii) the volatility spillover from exchange rate

changes to stock returns are not significant for all countries. Yang and Doong (2004) explore

the nature of the mean and volatility transmission mechanism between stock and foreign

exchange market for the G-7 countries and they find the asymmetric volatility spillover effect

and show that movements in stock prices will affect future changes of exchange rate

movements but not vice versa. In a more recent study, Walid et al. (2011) prove the evidence

that exchange rate returns have an influence on stock market volatility in four emerging

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markets (Hong Kong, Singapore, Malaysia, and Mexico) by employing Markov-Switching

EGARCH model. They also find the regime dependence between stock and foreign exchange

markets and asymmetric reactions of stock price volatility to the innovation of the foreign

exchange market.

Third group of studies focuses on causality test and cointegration analysis. Ajayi and

Mougoue (1996), using an error correction model (ECM) of the stock price and exchange rate

for the Big-eight countries, finds significant short-run and long-run feedback relations

between the two financial markets, i.e., an increase in aggregate domestic stock price has a

negative short-run effect and positive long-run effect on domestic currency value. However,

currency depreciation has negative short-run and long-run effect on the stock market (April

1985-July 1991). Granger et al. (2000) investigate causality and vector autoregressive (VAR)

analysis using Asian flu data. They find that exchange rates lead stock prices in Korea, but

stock price lead exchange rates in Philippines. Whereas they find feedback relations from

Hong Kong, Malaysia, Singapore, Thailand and Taiwan, they cannot find any patterns in

Japan.

Nieh and Lee (2001), using the cointegration analysis, find that there is no long-run

significant relationship between stock prices and exchange rates in the G-7 countries.

However, there is short-run (one-day) significant relationship in several countries. Lean et al.

(2005) study the cointegration and the bivariate causality relationship between exchange rates

and stock prices on the seven Asian countries badly hit by the Asian Financial Crisis. Their

empirical results show that, before the 1997 Asian Financial Crisis, all countries, except the

Philippines and Malaysia, experienced no evidence of Granger causality between the

exchange rates and the stock prices. However, the causality, but not the cointegration,

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between the capital and financial markets appeared to become strong during the Asian

Financial Crisis period. Surprisingly, after the 911-terrorist-attack, the causality relationship

between the two markets returned to normal as in the pre-Asian-crisis period and the

cointegration relationship weakened between exchange rates and stock prices. Phylaktis and

Ravazzolo (2005) study the long-run and short-run dynamics between stock prices and

exchange rates and the channels through which exogenous shocks impact on these markets by

using cointegration methodology and multivariate Granger causality tests. They apply the

analysis to a group of Pacific Basin countries over the period 1980-1998 and conclude that

stock and foreign exchange markets are positively related and the US stock market acts as a

conduit for these links. Kanas (2005) uses Markov-Switching VAR model in order to explore

the linkage in volatility regimes between the Mexican currency market and six emerging

equity markets. The evidence supports that the probability of the Mexican currency market

being in the high-volatility regimes causes the probability of equity markets in Mexico, Brazil,

Argentina, and Hong Kong being in the high-volatility regime.

III. DCC-MGARCH Model and Estimation

A. Data and Descriptive Statistics

In the empirical study, we use daily data of the stock prices, the exchange rates, the

interest rates, CDS spreads, the stock volatility index, and FX volatility index for 6 OECD

countries: Australia, Canada, Japan, Switzerland, UK and US. We collect data from

Bloomberg and Datastream, which cover from January 2, 2006 to December 31, 2010. Data

Appendix presents detailed sources and definitions of each data used in this study. The

exchange rates show the purchasing power of local currency in terms of US dollar. For US,

9

the quotation is Euro per unit of US dollar. While Figure 1 plots exchange rates and their

returns, Figure 2 depicts stock index and stock price returns for 6 countries.

[Figure 1, 2 about here]

The figures reveal that the volatility of both the stock price return and the exchange

rate return increased rapidly during the 2008 US financial crisis period. Also, it is shown that

there are huge crashes in national stock index for all markets around middle of 2008.

However, the movements of exchange rates during the same period seem to be different

among countries.

Table 1 shows the descriptive statistics for exchange rate returns and stock returns.

From the Panel A of Table 1, we can see that UK and US have negative sample mean of -0.7 %

and -1 % in their exchange rate returns, while Japan has the maximum mean value of 3.6 %.

Variance is highest in Australia (standard error of 1.104) but lowest in US (standard error of

0.686). All countries’ return data reveal heteroscedasticity and are not normally distributed.

Panel B presents summary statistics for the stock market returns. During the sample period,

Canada has the highest mean returns (0.014 %) while Japan has the lowest mean return (-

0.047 %). On the other hand, volatility is highest in Japan but lowest in Switzerland. Similar

to exchange rate returns, all countries show heteroscedasticity in their stock return series.

[Table 1 about here]

B. Unit Root Test and Cointegration Test

Whereas traditional Augmented Dickey–Fuller test (ADF) or Phillips-Perron (PP)

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tests of unit root do not allow the possibility of abrupt changes in series, the unit root tests

with the structural break are able to take account of them. Since our study focuses on the

subprime mortgage crisis in 2008, which caused radical changes in financial market, it is

rational to include a structural break in testing the existence of unit root. By employing the

Lagrangian multiplier (LM) unit root test of Lee and Strazicich (2004), we try to analyze the

stationarity of each series in crash model, which allows only change in intercept, and break

model, which includes change in trend as well as in intercept, as following:

(1) 0 1 2 3 11

,k

t t t t j t j tj

y t B B t y c y eα α α α β − −=

= + + + + + Δ +∑

where , , and t tt B e are time trend, the change in intercept, and error term, respectively.

Equation (1) describes break model, and without fourth term, which denotes the change in

trend, it implies crash model.

Table 2 shows that we cannot reject the null hypothesis of nonstationarity in the level

of the exchange rate and the stock price in all countries, but reject in their first differences

under 1% significance level. Thus, we conclude that the exchange rate and the stock price in

all countries are I(1) process.


In order to consider the long-term relationship between two financial markets, we

analyze the cointegration test using the methodology of Gregory and Hansen (1996). Similar

to the unit root test, Gregory-Hansen tests is advantageous to reflect the structural break.

Table 3 depicts the result of the cointegration test in the following equation:

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(2) 1 1 2 1 2 2 2 ,t t t t t ty t y y eτ τμ μ ϕ β α α ϕ= + + + + +

where 1 2, , , and tt eμ μ signify the intercept before the break, the change in the intercept at the

break, time trend, and error term, respectively, and 1 2, , , and tτϕ α α β denotes the coefficient

of level shift, the cointegrating slope before the break, the change in the slope, and time trend

respectively.


Depending on which term is included in the model, we divide the results into model

C (constant), C/T (constant and trend), C/S (constant and slope), and C/T/S (constant, trend,

and slope). All models include LIBOR to control the international liquidity in the

cointegrating system. According to Table 3, it is shown that for Australia, Canada, Japan, and

UK, the null hypothesis of no cointegration between the stock price and the exchange rate is

rejected with any of four different specifications of the test. On the other hand, we cannot

reject the null hypothesis for Switzerland and US.

C. DCC-MGARCH Model

1. Model Specification

Engel (2002) proposes the dynamic conditional correlations model to estimate

conditional covariance in the Multivariate GARCH (MGARCH) model. This model is

advantageous by reducing the number of parameters in variance equations and allowing time

varying correlations in volatilities between variables to be derived. The conditional

covariance matrix in the DCC specification can be written as:

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(3) ,t t t tH D R D=

where ,( )t i tD diag h= is m m× diagonal matrix, where tD , following the univariate

GARCH(p, q) model, is defined as:

(4) 2, , ,

1 1

,i iP Q

i t i ip i t p iq i t qp q

h hω α ε β− −= =

= + +∑ ∑

and { }t ij tR ρ= is the time varying conditional correlation matrix:

(5) * 1 * 1,t t t tR Q Q Q− −=

where 1 1 1 1

(1 ) ( ' )M N M N

t m n m t m t m n t nm n m n

Q Q Qα β α ε ε β− − −= = = =

= − − + +∑ ∑ ∑ ∑ ,

and Q is the

unconditional covariance of the ,i jε and ,i jε , and *,{ }t i iQ diag q=

is a diagonal matrix

contains the square root of the diagonal elements of tQ .

The correlation estimator of tQ is:

(6) ,,

, ,

, for , 1, 2, ... , n and .ij tij t

ii t jj t

qi j i j

q qρ = = ≠

For maximizing the log-likelihood function:

(7) ' 1

1

1 [ log(2 )] 2 log log2

T

t t t t tt

L m D R Rπ ε ε−

=

=− + + +∑ ,

we can get the estimation of the DCC model.

In this study, we develop the DCC-MGARCH(1,1) of stock price returns and

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exchange rate returns. The mean equations are defined in the following manner:

(8) 0 1, 2, 1,1 1

,K K

t j t j j t j tj j

STR STR FXRγ γ γ ε− −= =

= + + +∑ ∑

(9) 0 1, 2 1 2,1

,K

t j t j t tj

FXR STR FXRλ λ λ ε− −=

= + + +∑ .

where and t tSTR FXR are stock price returns and exchange rate returns, and 1, 2, and t tε ε are

heteroscedastic error terms of each equation. In the conditional variance equations, we allow

the model to include asymmetric effects based on a GJR threshold type formulation (Glosten

et. al. (1993)) and EGARCH (Nelson (1991)). It is assumed that the volatility raises

proportionally more following negative shocks than positive shocks. Thus, the conditional

variance equations can be written as:

(10) 1

2, 1 1 1, 1 1 , 1 1 1, 1 0 1, ,

tSTR t t STR t t th c h d Iεα ε β ε υ−− − − <= + + + +

(11) 1

2, 2 2 2, 1 2 , 1 2 1, 1 0 2, ,

tFXR t t FXR t t th c h d Iεα ε β ε υ−− − − <= + + + +

where , , and STR t FXR th h are volatility terms of stock price returns and exchange rate returns,

1, 2, and t tε ε are from Equation (8) and (9), and 1, 2,and t tυ υ u, follows white noise processes.

The fourth term of Equation (10) and (11) implies asymmetric effects; I takes unity, when

the innovative shock on 1 tε − is negative, and zero otherwise.

2. Estimation of DCC-MGARCH Model

Estimation results from the DCC-MGARCH model presented in Table 4. We observe

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that lagged exchange rate returns in the stock return mean equation are negative and

significant for Japan and Switzerland, while positive and significant for Australia and Canada.

However, it is shown that lagged exchange rate returns in the stock return mean equation are

insignificant for UK and US. On the other hand, the lagged stock returns in the exchange rate

return mean equation is negative and significant for US, positive and significant for Canada,

but insignificant for others.


Looking at the variance equations, we find that all of the coefficients for the squared

error and the lagged variance are positively significant in both stock return and exchange

return equation for 6 countries. This validates the appropriateness of the DCC-GARCH

specification. Positively significant coefficients of A(1) and A(2) support the idea that the

shocks from each market may boost volatility in that market. Large value of estimated

coefficient in the lagged own variance term indicate that shocks have persistent impact.

Moreover, asymmetric terms in the conditional variance of stock market returns show all

positive and significant association to their volatility, implying that negative shocks in stock

market may cause larger volatility than positive ones. On the other hand, asymmetric effects

in foreign exchange markets are significant only in Australia, Canada, and UK. Those are

negatively significant in Japan, while not significant in Switzerland and US.

3. DCCs of 6 OECD Countries

Table 5 presents the summary statistics for DCCs between stock market returns and

foreign exchange returns in 6 countries. We can see that Australia (0.212), Canada (0.444)

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and UK (0.245) has a positive mean value of DCCs, while that for Japan (-0.305),

Switzerland (-0.035) and US (-0.256) are negative on average. However, all DCCs show

heteroscedasticity and deviation from normality.


Figure 3 shows estimated DCCs of 6 OECD countries. Consistent with Table 5, DCCs are

mostly negative for US and Japan. However DCCs of Switzerland negative before the crisis

but become positive after the US financial crisis. Other three countries (Australia, Canada

and United Kingdom) have positive DCCs throughout the period.

[Figure 3 about here]

From Figure 3, we can see that DCCs increase abruptly near the Lehman failure (contagion

phase of the crisis defined in the next section) for all countries. Since DCCs are negative in

US and Japan, their absolute values of DCCs increase during the contagion period. This

implies that substitution effects (Friedman (1988), and Choudhry (1996)) are stronger than

wealth effect in US and Japan for the most of the periods. However, if we focus on the

contagion and post-crisis adjustment phases of Switzerland, DCCs become positive and this

implies that huge decrease in stock returns cause decrease in exchange rate returns

(dominance of wealth effect). On the other hand, United Kingdom, Canada, and Australia

have positive DCCs for the most of the periods and this implies that wealth effect dominates

substitution effect in those countries.

IV. Changing Patterns of Dynamic Interactions

In this section, first of all, we estimate different phase of financial crisis for 6 OECD

16

countries by employing Bai-Perron test of unknown structural breaks for each country’s

DCCs. Using structural breaks found by Bai-Perron test, we investigate changing patterns of

Granger causality between stock market and foreign exchange. To find robustness of

structural breaks, we analyze GARCH with dummy variables model. Finally, we use Markov

regime-switching causality test to find out why exchange rate changes lead stock returns

during the contagion phase of the financial crisis.

A. Structural Breaks in DCCs: Bai-Perron Test

To investigate changing phases of interactions between two financial markets during

the US financial crisis, we estimate unknown structural breaks of DCCs using Bai-Perron test

(Bai and Perron, 1998). For this test, we use the equation (12):

(12) 1t j j t ty c yβ ε−= + +

where 1 1, , ,j jt T T−= + … 1, , 1j m= +… , 1, , mT T… are the break points, and m is the

number of breaks. In this model, we assume all the coefficients are subject to change over

time. This method sequentially proceeds the test by increasing the number of breaks. In other

words, if the test finds one structural break in the whole sample period, then it repeats the

same process in two subsamples, before and after the break. This recursive process continues

until any subsamples do not have significant structural break.


We set the number of maximum structural break as 6 and the shortest distance

between two breaks are 60. Table 6 shows the estimation results of the Bai-Perron test for

DCCs. From Table 6, Canada and Japan has 4 structural breaks while other countries have 3

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structural breaks. From Table 6, we can see that all countries have a structural break around

September and October of 2008, which may be caused by the Lehman failure in the mid-

September. Using those structural breaks in DCCs, we divide the sample into three distinctive

sub-periods, i.e., before-crisis period, contagion period and post-crisis adjustment period. For

Japan, we find a break at January 5, 2007 when the NIKKEI plunged 10.72% in December 29,

2006. For US, we find a break at August 9, 2007 where DJIA fell 400 points in that day. On

the other hand, the break at January 29, 2009 in US and that at January 7, 2009 in Australia

matches the US government and Australian Senate approval of a stimulus package.

B. Sub-Sample Granger Causality Test

Table 7-B reports Granger causality test of the stock returns and exchange rate

changes for each sub-periods.


From Table 7, during the pre-crisis period, US shows the lead of stock returns and

Japan shows the lead of exchange rate changes while Australia and Switzerland have bi-

directional causality. However, during the contagion period, Australia, Canada, Japan, and

Switzerland show the lead of exchange rate changes but US and UK do not show any

causality at all. Finally, during the post-crisis adjustment period, Australia shows the lead of

exchange rate changes and US returns to their pre-crisis period patterns of lead of stock

returns and Japan shows bi-directional causality. However, Canada, Switzerland and UK do

not show any causal relations at all. From this analysis, we can say that the lead of exchange

rate changes is prominent during the contagion period of the crisis. In other words, we can

say that the lead of foreign exchange market increases significantly after the US financial

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crisis implying that across-the-border capital flows (flight for quality) increase significantly

after the US financial crisis and this increase the volatility of exchange rates and those

changes in exchange rates are priced in domestic stock market.

From Table 7-A, during the pre-crisis period, advanced economies as a whole, stock

returns lead foreign exchange returns 4 out of 12 sub-periods while foreign exchange returns

lead stock returns 2 out of 12 sub-periods. However, after the October 2008, stock returns

lead foreign exchange returns 1 out of 14 sub-periods while foreign exchange returns lead

stock returns in 6 out of 14 sub-periods.

C. Markov-Switching Granger Causality Test

While Granger causality test does explain causal directions between two variables it cannot

explain why causal directions are changing in different phases of financial crisis. By applying

the regime switching approach (Hamilton (1989)), it is possible to find under what situation

(regime) exchange changes lead stock returns or vice versa.


In this section, we investigate the Markov-Switching Granger causality test with the

Markov chain Monte Carlo (MCMC) method (Krolzig (1997)):

(13) ( ) ( ) ( )

0 1, 2, 1,1 1

,t t t

K Ks s s

t j t j j t j tj j

STR STR FXRγ γ γ ε− −= =

= + + +∑ ∑

(14) ( ) ( ) ( )0 1, 2 1 2,

1

,t t t

Ks s s

t j t j t tj

FXR STR FXRλ λ λ ε− −=

= + + +∑

19

(15) 1, ( )

2,

~ . . (0, ),tt s

t

i i Nε

ε⎡ ⎤

Σ⎢ ⎥⎣ ⎦

where ts is an indicator variable for each regime of the system at time t and takes either

value in the set {1, 2}, and covariance matrices, ( )tsΣ , depend on the regimes 1,2.ts =

Moreover, the probability transition from one state to another is governed by the probability

transition matrix defined as:

(16) 11 12

21 22

p pP

p p⎡ ⎤

= ⎢ ⎥⎣ ⎦ .

When 1ts j− = , the time-invariant transition probability of moving to ts i= can be written

ijp .

There are two advantages of using the MCMC method. First of all, the hidden states

of the MCMC method could be interpreted as high variance regime or low variance regime.

In this way, we can analyze how the causality between the stock returns and the exchange

rate changes is changing in the crisis period (the high variance regime) and the non-crisis

period (the low variance regime). Second, Gibbs sampling1 (Casella at al., 1992: Kim et al.,

1999) allows us to be able to estimate traditional ML estimation with exponentially increased

number of parameter. In the estimation procedure, we first use the Forward Filter-Backward

Sampling (FFBS) algorithm (Chib (1996)) to draw the likelihoods across regimes. Given the

1 This sampling approach is clearly advantageous, since it enables us to estimate several low-dimensional estimations, instead of one high-dimensional function. To make sure that the results from the Gibbs sampling indeed close enough to a random sample from the joint distribution, we run 5,000 simulations and drop out first 2,000 results as burn-ins.

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regimes, Gibbs sampling2 produces the simulations of following parameters in the function:

(17) ( ), , ,i i j if X Mθ θ ≠

where iθ is the model parameter to be estimated, X is the data, and M is the model. Equation

17 is defined as the conditional distribution of the parameter iθ . In order to derive the

conditional posterior distributions, we assume the prior distribution for the model to be the

Wishart distribution, which is a multi-dimensional version of the chi-square distribution. By

using the Bayesian inference in the following equation, we derive the conditional posterior

distributions:

(18) ( ) ( ) ( )( )

,f X P

f Xf Xθ θ

θ =

where ( )P θ is the prior of the Wishart distributions. The posterior distribution is a

multivariate normal distribution which belongs to the same family of the prior distribution,

indicating that the Wishart distribution is the conjugate prior distribution.

From the earlier procedures, it is possible to obtain the point estimation of means and

corresponding variances for the parameters, thereby enabling us to test the significance by

using t-statistics.

2. Estimation of Markov-Switching Granger Causality Test

2 This sampling approach is clearly advantageous, since it enables us to estimate several low-dimensional estimations, instead of one high-dimensional function. To make sure that the results from the Gibbs sampling indeed close enough to a random sample from the joint distribution, we run 5,000 simulations and drop out first 2,000 results as burn-ins.

21

The estimation results of Markov-Switching VAR models for 6 advanced markets are

reported in Table 8. First of all, we check if estimated regimes are in line with the

presupposed division of the whole sample period into the high variance period and the low

variance period. In Table 8, except Switzerland, all the elements of the estimated covariance

matrix between the stock market returns and the exchange rate changes, i.e., COV(i, j) in the

third panel of table 9, show significant results for all countries. Among all variances and

covariances that are significant, the coefficients in the high variance regime are always

greater than those in the low variance regime, implying that the regimes are well divided into

the high variance regime and low variance regime during the US crisis around 2008.


In Figure 4, we show the estimated smoothed probabilities3 of the high variance

regime (solid line) to compare those probabilities with the market volatilities4 derived from

the DCC-MGARCH model in the section 3 (two dotted lines).

[Figure 4 about here]

While volatilities of stock market and foreign exchange market move together, the smoothed

probabilities of high variance regime can successfully identify (local or global) peak points of 3 The smoothed probability at t, given data through the end of sample T , is defined as follows:

1

1

( )1|( ) ( )

| | ( )1 1|

, t

t t

t

s iMt Ts j s j

t T t t ij s ii t t

pp p p

p

+

+

=+= =

== +

= ∑

where M is the number of possibility for each St , |pt t is the filtered probability at t give data through t,

1|pt t+ is predicted probability at t+1 given data through t.

4 The values of volatilities are converted into a logarithm.

22

the GARCH volatilities. To check if smoothed probabilities of MCMC moves together with

the market volatilities estimated by GARCH model, we run and report a simple regression of

market volatilities on smoothed probabilities in table 9.


From table 9, we can see that the log of the volatilities of stock returns and the exchange rate

changes are highly significant in explain the movement of smoothed probabilities for all 6

countries. In other words, we can define high variance regime is a state when market

volatilities (estimated by GARCH) are high and low variance regime is the state when market

volatilities are low.

To test Granger causality with regime switching model, we utilize the Bonferroni and

Scheffe statistics (Savin (1980), and Psaradakis et al. (2005)). For the Bonferroni procedure,

B is defined as 2tδ , where

( )2 qδ α= × , α is the significance level, and q is the number

of parameters in the block. For the Scheffe procedure, S is defined as ( )( )1 2,q F q T k× − ,

where T k− is the number of free variables.

Table 10 reports the Bonferroni statistic and the Scheffe statistic for testing the null

hypotheses of the Markov-Switching Granger causality. It is shown that the Markov-

Switching Granger causality results of the high variance period are consistent with the results

of subsample VAR during the contagion period (the darkened area in Table 7), except for the

US exchange market. It is shown that two (Australia and Japan) out of six countries show the

Granger causality from the exchange market to the stock market in the low variance period, 5

out of 6 countries show the Granger causality from the exchange market to the stock market

23

in the high variance period. In addition to that, the lead of the stock market observed in

Switzerland during the low variance period disappears in the high variance period and

consequently no country reports the lead of stock market over the exchange market in the

high variance period. Summarizing, we can confirm that the dominance of the foreign

exchange market over the stock market during the contagion phase of the crisis period. In

other words, when market is relatively volatile, the exchange rates changes lead stock return

changes but not vice versa.


D. GARCH with Dummy Variables Model

To check the validity of changing phases of correlations and volatilities analyzed in section

IV.A – section IV.C., we use GARCH with dummy variables model.


To validate the changing phases of DCCs in previous sections, we employ

GARCH(1,1) model with time dummy variables, which is determined by different structural

breaks in Table 6. Since we focus on the US financial crisis, we drop the structural breaks that

happened before the US financial crisis. The model can be written as the following mean

equation (19) and the conditional variance equation (20):

(19) 0 1 1 1, ,1

,n

t t k k tk

DM ρρ γ γ ρ τ ε−=

= + + +∑

24

(20) 2

, , 1 , 1 2, ,1

,n

t t t k k tk

h c h DMρ ρ ρ ραε β τ υ− −=

= + + + +∑

where, 4n = for Canada and Japan, 3 otherwise. DMk is a time dummy variable for regime k.

2. Estimation of GARCH with Dummy Variables Model

Table 11 reports estimation results for GARCH with dummy variables model. From Table

11, we can see that estimated coefficients for dummy variables are highly significant for most

of the cases implying that interactions between stock returns and exchange rate changes are

changing over time.


From the estimates of DM1-DM4, we can classify 6 OECD countries into three distinct

groups of countries. First of all, DCCs of Australia, Canada and United Kingdom are positive

for the whole sample period and this implies that wealth effects are greater than substitution

effect in those countries. At the same time, DCCs of Switzerland are positive during and after

the contagion period. For this group of countries, DCCs increase with the US financial crisis

and the sign of estimated coefficients of dummy variable (DM2) for the contagion period are

positive and significant except Australia. However, Japan and US show that DCCs between

stock returns and exchange rate changes decrease (increase in absolute value) throughout the

crisis period and the rate of decrease is accelerating as they move from pre-crisis period to

contagion period (DM2) and from contagion period to post-crisis period (DM3). Since those

countries’ DCCs are negative for the most of the period, their conditional correlations

between stock returns and exchange returns strengthens during the contagion and post-crisis

period and this implies that substitution effects are stronger than wealth effect. However, if

25

we focus on early stage of contagion period in US, conditional correlations are positive and

this implies that huge decrease in stock returns caused dominance of wealth effect at the

beginning of the crisis. Finally, Switzerland has significant and positive DM2 and DCCs are

positive in contagion phase of the US financial crisis and remain positive during the post-

crisis adjustment period implying that wealth effect dominates substitution effect in the post-

crisis adjustment period. From the estimated variance equations in the lower panel, we can

also confirm that volatilities are changing from one period to the other and this validates our

analysis of “changing phases of correlations” between the stock returns and exchange rate

changes during the US financial crisis period.

V. Determinants of DCC between Stock Market and Foreign Exchange Market

A. DCCX Model and Explanatory Variables

DCCs derived from DCC-MGARCH model between stock price returns and

exchange rate returns in Equation (6) represent the size of the conditional correlation. In this

setting, it is important to identify which factors may determine the conditional correlation

between stock market and exchange market. Similar to DCCX model of Min and Hwang

(2010), we estimate the determinants of DCC in such function:

(21) ,,

,

exp( ' ),

1 exp( ' )i t

i ti t

XX

βρ

β=

+

where , ,andi t i tXρ are DCC and explanatory variables to DCC of each country. We take

absolute values of DCC because we investigate the effect of exogenous variables on the

strength of its comovement regardless of the direction. This logistic function is to circumvent

26

the restriction on DCC, being ,0 1i tρ≤ ≤ . Also, ( 1) vector tK X× includes VIX, FX VIX,

TED spread and CDS spread5. Therefore, the random effect model is defined as:

(22) ( ), 0 1 2 3 , 4 , ,i t t t i t i t i i tl VIXUS FXVUS TED CDS u eρ β β β β β= + + + + + +

where ( ),i tl ρ is the transformed DCC and ,and i i tu e are country-specific effect and error

term that follows white noise process.

Since Kanas (2000) argue that the strength of volatility spillovers seems to increase

in the crisis period, the VIX and FXV are included in the model. CDS spread implies global

macroeconomic factors as well as country specific risk factors (Longstaff et al. (2011)) and

plays a key role in credit contagion (Jorion and Zhang (2007)). Therefore, the model includes

CDS spread to take into account risk premium in each country to determine the conditional

correlation. TED spread, defined by the interest rate of each country less LIBOR, is included

to consider the effect of liquidity risk on the conditional correlations. Higher TED spread

implies tighter liquidity in economy (Lashgari (2000), and Cheung et al. (2010)).

B. Estimation of DCCX Model

Table 12 shows the test results of unit root and cointegration. In panel A of Table 12,

we cannot reject the null hypotheses of nonstationarity for all variables. However, we find the

cointegrated relations among variables in panel B of Table 12.

5 Data Appendix provides the detailed description of variables and their sources.

27


Table 13 reports the estimation results of DCCX model for 6 countries. First of all, it

is shown that the VIX index increase DCCs of stock returns and exchange rate changes. This

means that stock market volatility can spillover into the foreign exchange market as shown by

Kanas (2000). Second, Foreign exchange market volatility measured by FXV is insignificant.

Third, TED spread, which is a measure of liquidity, increases DCCs of stock returns and

exchange rate changes. This is consistent with the notion that increased TED spread, or

worsened liquidity would lower the stock market returns which then depreciate domestic

currency. In other words, the TED spread can strengthen the DCCs between stock price

returns and foreign exchange returns. Finally, CDS spread has negative and significant

association with DCCs and this is consistent with Bystrom (2005) that increased CDS spread

associated with increased volatility in stock market may strengthen the conditional

correlation.


VI. Conclusions

In this paper, we investigate the changing patterns of dynamic correlations between

stock market returns and exchange rate changes for the six OECD countries for the period of

January 2006-December 2010. First of all, using DCC-MGARCH model, we estimate

conditional correlations of stock market returns and exchange rate changes. Estimated DCCs

show that the substitution effect dominates wealth effect in US and Japan while the wealth

effect is stronger in United Kingdom, Canada, and Australia. Second, using Bai-Perron test

28

and Markov-Switching model, we estimate different phases of regime switching

corresponding to each sovereign country’s financial markets during the crisis. Also, from

Granger causality tests, we find that exchange rate changes Granger cause the stock returns

during the contagion phase of the US financial crisis for Australia, Canada, Japan,

Switzerland, and US. Third, using GARCH with dummy variables model, we confirm the

changing phases of dynamic correlations between the stock returns and exchange rate

changes. It is shown that while DCCs between stock returns and exchange rate changes are

increasing in US and Japan after the Lehman failure, those for Canada, United Kingdom and

Australia decrease during the contagion period but increase during the herding or post-crisis

adjustment period. Finally, using DCCX model, we report that VIX index and TED spread

increase conditional correlations of two markets, but CDS spread decreases the dynamic

correlations between stock returns and exchange rate changes.

Contrary to previous studies which fail to reflect the difference in macroeconomic

factors of each sovereign market, our empirical study identifies the framework for different

phases of dynamic linkages on FX markets and equity markets for 6 OECD countries during

the financial crisis in 2008. For investors and portfolio managers, our results provide better

chance to guard against their portfolios from the market turmoil in the future and

consequently improve financial strategies. Furthermore, this study can provide policy makers

with insights into the transmission channels that affect the strength of time varying

correlations between stock market and foreign exchange market and then allow them to

accommodate the policy to stabilize the financial market throughout the preemptive and

active responses against shocks in the market.

29

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33

TABLE 1

Descriptive Statistics

Table 1 reports the descriptive statistics of data. ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively. Panel A. FX Market Returns

Australia Canada Japan Switzerland UK US

Observations 1304 1304 1304 1304 1304 1304

Sample Mean 0.025 0.012 0.036 0.026 -0.007 -0.010

Standard Error 1.104 0.756 1.037 0.702 0.698 0.686

t-Statistic (Mean=0) 0.831 0.564 1.248 1.349 -0.386 -0.500

Skewness -0.729*** -0.214*** 0.691*** 0.235*** -0.512*** -0.152**

Kurtosis (excess) 12.021*** 2.400*** 6.873*** 2.562*** 2.796*** 2.256***

Jarque-Bera Statistics 7967.0*** 323.0*** 2670.6*** 368.5*** 481.6*** 281.4***

Autocorrelation Test

Ljung-Box Q Test 22.036*** 11.529** 19.764*** 3.116 4.333 1.289

Heteroscedasticity Test

ARCH(15) LM Test 39.23*** 25.691*** 22.896*** 8.879*** 22.432*** 17.564*** Panel B. Stock Market Returns


Observations 1304 1304 1304 1304 1304 1304

Sample Mean 0.000 0.014 -0.047 -0.013 0.004 0.001

Standard Error 1.334 1.457 1.605 1.317 1.447 1.546

t-Statistic (Mean=0) 0.002 0.335 -1.048 -0.345 0.093 0.013

Skewness -0.446*** -0.675*** -0.205*** 0.116* -0.093 -0.236***

Kurtosis (excess) 4.170*** 8.237*** 7.068*** 7.866*** 7.324*** 9.013***

Jarque-Bera Statistics 987.7*** 3785.3*** 2723.7*** 3364.6*** 2916.6*** 4426.3***


Ljung-Box Q Test 8.584 37.604*** 11.482** 37.842*** 44.642*** 37.016***


ARCH(15) LM Test 26.292*** 46.934*** 55.431*** 41.031*** 30.749*** 44.907***

34

TABLE 2

Result of Unit Root Test

Table 2 reports the LM unit root test with a structural break. The optimal number of lags in each series is determined by Akaike information criterion (AIC). ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively.

Country Variable Crash Model Break Model

Break Point # of lags t-statistics Break date # of lags t-statistics

Panel A. Level

Australia Exchange Rate 2008:10:23 7 -1.878 2008:09:12 7 -2.57032

Stock Index 2008:10:09 0 -1.500 2008:07:02 0 -2.20266

Canada Exchange Rate 2008:10:21 9 -2.002 2008:10:03 9 -2.52661

Stock Index 2008:10:24 10 -1.583 2008:09:26 5 -2.82188

Japan Exchange Rate 2008:10:03 7 -1.717 2008:10:21 7 -2.56477

Stock Index 2008:09:15 2 -1.746 2008:11:05 0 -2.84418

Swiss Exchange Rate 2008:09:29 10 -2.910 2008:09:22 10 -3.84986

Stock Index 2008:10:21 5 -1.321 2008:10:16 2 -2.04937

UK Exchange Rate 2008:11:28 10 -1.149 2008:09:03 10 -2.06085

Stock Index 2008:10:23 4 -1.610 2008:09:26 4 -2.98737

US Exchange Rate 2008:12:18 8 -2.103 2008:08:25 8 -3.2199

Stock Index 2008:11:28 7 -1.273 2008:09:16 2 -2.25891

Panel B. Log Return

Australia Exchange Rate 2009:03:03 10 -10.380*** 2010:05:24 6 -13.779***

Stock Index 2009:02:23 8 -10.675*** 2007:01:03 0 -37.513***

Canada Exchange Rate 2008:11:03 8 -13.123*** 2007:10:29 8 -13.357***

Stock Index 2009:03:16 9 -8.716*** 2009:07:09 9 -11.820***

Japan Exchange Rate 2009:03:05 4 -15.227*** 2008:01:04 4 -15.260***

Stock Index 2009:03:02 10 -10.680*** 2007:12:26 10 -10.937***

Swiss Exchange Rate 2008:12:16 10 -4.238*** 2008:09:17 9 -10.501***

Stock Index 2009:02:18 9 -12.024*** 2007:05:18 6 -15.997***

UK Exchange Rate 2008:07:25 6 -12.310*** 2009:04:10 10 -13.338***

Stock Index 2010:06:11 1 -27.656*** 2010:02:09 1 -27.648***

US Exchange Rate 2008:09:01 9 -12.749*** 2006:08:15 6 -13.489***

35

Stock Index 2008:12:26 0 -35.574*** 2008:08:11 0 -35.667***

TABLE 3

Result of Cointegration Test

Table 3 reports the Gregory-Hansen cointegration root test with a structural break. The optimal number of lags in each series is determined by AIC. ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively.

Country Model C Model C/T Model C/S Model C/T/S

Australia Break Point 2008:01:22 2008:10:14 2008:01:25 2008:08:18 # of Lags 2 2 2 2 t-Statistics -3.909 -5.429** -4.773 -6.25**

Canada Break Point 2007:08:20 2007:08:20 2007:06:12 2007:06:08 # of Lags 1 1 1 1 t-Statistics -4.45 -4.716 -5.302** -5.544

Japan Break Point 2009:03:03 2009:02:27 2009:01:21 2009:02:27 # of Lags 3 1 5 1 t-Statistics -3.897 -5.102** -4.111 -6.708**

Switzerland Break Point 2008:01:04 2008:09:19 2008:01:08 2008:07:14 # of Lags 1 1 5 2 t-Statistics -3.776 -4.187 -4.311 -4.393

UK Break Point 2010:02:11 2010:02:11 2008:10:27 2009:06:04 # of Lags -4.365 -4.979 -5.086** -5.597 t-Statistics 1 1 1 1

US Break Point 2007:10:19 2010:02:08 2008:10:08 2008:10:08 # of Lags 0 0 0 1 t-Statistics -3.226 -4.124 -4.257 -4.839

36

TABLE 4

Estimation Results from the DCC-GARCH(1,1) Model

The panel A shows the estimation results of mean equations ( ,0 1, 2, 1,1 1

K KSTR STR FXRt j j tt j t j

j jγ γ γ ε= + + +∑ ∑− −

= =0 1, 2 2,1

1

KFXR STR FXRt j tt j t

jλ λ λ ε= + + +∑ − −

=) and the panel B presents the

estimation results of variance equations ( 2 ,, 1 1 1 , 1 1 1, 1 0 1,1, 1 1h c h d ISTR t STR t t tt tα ε β ε υε= + + + +− − <− −2

, 2 2 2 , 1 2 2, 1 0 2,2, 1 1h c h d IFXR t FXR t t tt tα ε β ε υε= + + + +− − <− − ). Likelihood-ratio (LR) test examines the cross effects between stock price returns and exchange rate returns in mean equations. t-statistics are in parentheses. ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively. Panel A. Mean equations


Constant 0.038* 0.039* 0.020 0.041* 0.062** 0.068*** (1.698) (1.776) (0.695) (1.754) (2.544) (2.939)

STR{1} -0.141*** -0.064** -0.096*** 0.005 -0.070** -0.060** (-5.292) (-2.534) (-3.528) (0.191) (-2.53) (-2.079)

STR{2} -0.042* (-1.700)

FXR{1} 0.477*** 0.120*** -0.445*** -0.076* -0.021 0.006 (16.592) (3.336) (-15.249) (-1.905) (-0.470) (0.164)

FXR{2} 0.07** (1.991)

Constant 0.052*** 0.021 -0.023 0.025 0.014 -0.026* (3.200) (1.503) (-1.51) (1.629) (0.937) (-1.862)

FXR{1} -0.073*** -0.057** -0.004 -0.058** -0.013 -0.038 (-4.183) (-2.397) (-0.156) (-2.172) (-0.482) (-1.403)

STR{1} 0.022* 0.004 0.010 0.016 -0.033*** (1.841) (0.243) (0.705) (1.388) (-2.743)

37

Panel B. Variance equations


C(1) -0.142*** -0.112*** -0.101*** -0.162*** -0.169*** -0.126*** (-6.935) (-47.372) (-36.642) (-44.525) (-43.897) (-60.722)

C(2) -0.160*** -0.12*** -0.144*** -0.066*** -0.101*** -0.085*** (-8.158) (-51.44) (-71.145) (-57.465) (-49.983) (-54.042)

A(1) 0.168*** 0.141*** 0.141*** 0.197*** 0.224*** 0.169*** (6.233) (45.541) (38.246) (37.708) (43.918) (53.796)

A(2) 0.190*** 0.129*** 0.212*** 0.083*** 0.106*** 0.104*** (7.483) (42.651) (76.384) (56.632) (40.540) (50.691)

B(1) 0.955*** 0.975*** 0.963*** 0.949*** 0.965*** 0.977*** (87.574) (307.01) (251.572) (165.711) (194.107) (471.88)

B(2) 0.977*** 0.981*** 1.002*** 0.997*** 0.984*** 0.995*** (150.763) (404.758) (402.22) (866.424) (567.511) (747.698)

D(1) 0.018*** 0.008*** 0.009*** 0.02*** 0.009*** 0.006*** (3.209) (7.081) (8.558) (7.037) (4.770) (4.951)

D(2) 0.009** 0.018*** -0.027*** 0.000 0.016*** -0.003 (2.536) (3.035) (-8.36) (0.030) (3.298) (-0.528)

Log

Likelihood -3528.68 -3126.13 -3754.59 -3182.03 -3226.94 -3112.82

0 2 1

LR Test: 0H γ λ= =

275.288*** 18.517*** 232.646*** 4.229 2.149 7.552**

38

TABLE 5

Descriptive Statistics for DCC of Major Developed Countries

Table 5 presents the descriptive statistics for DCCs of major developed countries which are Australia, Canada, Japan, Switzerland, UK, and US. ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively.


Observations 1303 1303 1303 1303 1303 1303

Sample Mean 0.212 0.444 -0.305 -0.035 0.245 -0.256

Standard Error 0.000 0.165 0.166 0.184 0.000 0.220

t-Statistic (Mean=0) 68383157.924 97.195 -66.386 -6.820 696850.440 -42.091

Skewness 0.361*** -0.552*** 0.419*** -0.319*** -0.414*** 0.762***

Kurtosis (excess) -1.468*** -0.521*** 0.123 -0.266* -1.092*** -0.165 Jarque-Bera Statistics 145.3*** 80.8*** 38.9*** 25.9*** 101.9*** 127.7***


Ljung-Box Q Test 6429.035 6251.252 6227.765 6135.385 6483.81 6436.166


ARCH(15) LM Test 50703.08*** 19636.73*** 10619.68*** 6221.398*** 9618.383*** 33770.33***

39

TABLE 6

Estimation Results from Structural Breaks

Table 6 presents the result of Bai-Perron test of multiple structural breaks. The number of significant breaks in each DCC is determined by Bayesian information criterion (BIC). ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively.

Country # of Breaks Break Point Lower 95% Upper 95%

Australia 3

2008:07:22 2008:06:13 2008:07:22

2008:10:14 2008:10:13 2008:10:16 2009:01:07 2009:01:07 2009:02:26

Canada 4

2008:05:01 2008:04:28 2008:05:26

2008:09:04 2008:08:29 2008:09:19 2010:05:20 2010:04:30 2010:05:24 2010:08:30 2010:08:27 2010:09:27

Japan 4

2007:01:05 2006:08:24 2007:01:19 2008:10:06 2008:05:12 2008:10:07 2008:12:29 2008:12:26 2009:05:01

2010:05:11 2010:05:10 2011:01:20

Switzerland 3 2008:03:14 2007:08:30 2008:03:26 2008:10:03 2008:09:29 2008:10:08

2009:10:07 2009:09:15 2010:08:18

UK 3 2008:07:07 2007:10:04 2008:07:08 2008:10:22 2008:10:16 2008:10:24

2009:05:29 2008:06:09 2009:06:12

US 3 2007:08:09 2007:07:30 2007:08:15 2008:09:04 2008:08:14 2008:09:05

2009:01:29 2009:01:16 2009:03:17

40

TABLE 7

Estimation Results from the Granger Causality

Table 7 reports the result of sub-sample Granger causality test between stock price returns and exchange rate returns. The darkened area signifies the contagion phase of the crisis around September and October in 2008. B, S, E, and X in the first column stand for bidirectional relationship, lead of stock market, lead of foreign exchange market, and no causality, respectively. ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively. Panel A. Granger Causality Test for all structural breaks by Bai-Perron Break Country Causality F-Value P-Value F-Value P-Value F-Value P-Value F-Value P-Value F-Value P-Value

Australia (B-E-E)

Period 2006:01:02 2008:07:21 2008:07:22 2008:10:13 2008:10:14 2009:01:06 2009:01:07 2010:12:31

E-/->S 41.2792*** 0.000 6.2525*** 0.0036 11.568*** 0.0001 58.3547*** 0.000

S-/->E 2.8345* 0.0595 3.9148** 0.0257 1.2113 0.3055 2.0459 0.1065

Canada (X-E-X)

Period 2006:01:02 2008:04:30 2008:05:01 2008:09:03 2008:09:04 2010:05:19 2010:05:20 2010:08:29 2010:08:30 2010:12:31

E-/->S 0.7798 0.3775 2.3443 0.1294 12.1078*** 0.0000 0.0000 0.9945 0.2611 0.6106

S-/->E 0.8420 0.3592 1.2943 0.2584 1.0449 0.3526 0.5074 0.4786 0.0285 0.8663

Japan (X-E-E)

Period 2006:01:02 2007:01:04 2007:01:05 2008:10:05 2008:10:06 2008:12:28 2008:12:29 2010:05:10 2010:05:11 2010:12:31

E-/->S 0.1290 0.7198 54.5758*** 0.0000 12.7389*** 0.0007 67.0967*** 0.0000 7.4148*** 0.0001

S-/->E 0.7987 0.3723 0.9959 0.3188 0.7242 0.3983 0.8420 0.3594 2.0767 0.1054

Switzerland (E-B-S-X)

Period 2006:01:02 2008:03:13 2008:03:14 2008:10:02 2008:10:03 2009:10:06 2009:10:07 2010:12:31

E-/->S 3.4435* 0.0640 9.6401** 0.0023 2.3734** 0.0397 0.0165 0.8979

S-/->E 0.4554 0.5001 17.2786*** 0.0001 1.0466 0.3908 0.0675 0.7952

UK (S-X-X)

Period 2006:01:02 2008:07:06 2008:07:07 2008:10:21 2008:10:22 2009:05:28 2009:05:29 2010:12:31

E-/->S 0.5560 0.5738 0.1368 0.7125 1.0156 0.3151 0.2920 0.5893

S-/->E 6.1317** 0.0023 4.1414** 0.0454 0.0987 0.7539 0.1390 0.7095

US Period 2006:01:02 2007:08:08 2007:08:09 2008:09:03 2008:09:04 2009:01:28 2009:01:29 2010:12:31

41

(S-X-S) E-/->S 0.1047 0.7465 1.3223 0.2512 0.8461 0.3598 0.2249 0.6356

S-/->E 6.6807** 0.0101 8.3319** 0.0042 0.4371 0.5100 6.1565** 0.0134

Panel B. Granger causality Test for 3 periods (Pre-crisis, Contagion, and Post-crisis)

Country Causality F-Value P-Value F-Value P-Value F-Value P-Value

Australia (B-E-E)

Period 2006:01:02 2008:10:13 2008:10:14 2009:01:06 2009:01:07 2010:12:31

E-/->S 14.6174*** 0.000 11.568*** 0.0001 58.3547*** 0.000

S-/->E 7.3549*** 0.000 1.2113 0.3055 2.0459 0.1065

Canada (X-E-X)

Period 2006:01:02 2008:09:03 2008:09:04 2010:05:19 2010:05:20 2010:12:31

E-/->S 0.000 0.9928 12.1078*** 0.0000 0.0944 0.7591

S-/->E 1.3228 0.2505 1.0449 0.3526 0.1037 0.7478

Japan (E-E-E)

Period 2006:01:02 2008:10:06 2008:10:06 2008:12:28 2008:12:29 2010:12:31

E-/->S 52.6994*** 0.000 12.7389*** 0.0007 80.8344*** 0.000

S-/->E 1.3878 0.2392 0.7242 0.3983 3.0975* 0.0781

Switzerland (B-E-X)

Period 2006:01:02 2008:10:02 2008:10:03 2009:10:06 2009:10:07 2010:12:31

E-/->S 13.1593*** 0.000 2.3734** 0.0397 0.0165 0.8979

S-/->E 15.5661*** 0.000 1.0466 0.3908 0.0675 0.7952

UK (X-X-X)

Period 2006:01:02 2008:10:21 2008:10:22 2009:05:28 2009:05:29 2010:12:31

E-/->S 1.2579 0.2851 1.0156 0.3151 0.2920 0.5893

S-/->E 0.7507 0.5577 0.0987 0.7539 0.1390 0.7095

US (S-X-S)

Period 2006:01:02 2008:09:03 2008:09:04 2009:01:28 2009:01:29 2010:12:31

E-/->S 0.5845 0.4448 0.8461 0.3598 0.2249 0.6356

S-/->E 15.9739*** 0.000 0.4371 0.5100 6.1565** 0.0134

42

TABLE 8

Estimation Results of Markov-Switching VAR

Table 8 reports the result of Markov-Switching Granger causality test between stock price returns and exchange rate returns in Australia. COV(i,j) signifies each element of the covariance; COV(1,1) is the variance of the stock return equation, COV(2,2) is the variance of the exchange return equation, whereas COV(2,1) is the covariance of two equations. P(i,j) represents the probability of being in regime i at t, given that in regime j at t-1. The absolute values of t-statistics are in parentheses. ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively. Panel A. Australia

Low Variance Regime High Variance Regime

Variable Coefficient t-Statistics Variable Coefficient t-Statistics

Stock Return Equation

Constant 0.035 (1.129) Constant -0.162 (1.328)

STR{1} -0.166*** (4.743) STR{1} -0.189*** (3.048)

STR{2} -0.013 (0.406) STR{2} -0.052 (0.897)

FXR{1} 0.466*** (9.320) FXR{1} 0.470*** (7.231)

FXR{2} 0.070 (1.489) FXR{2} 0.203*** (2.859)

Exchange Return Equation

Constant 0.09*** (3.913) Constant -0.226* (1.915)

STR{1} 0.028 (1.077) STR{1} -0.048 (0.814)

STR{2} 0.000 (0.000) STR{2} -0.030 (0.536)

FXR{1} -0.082** (2.216) FXR{1} -0.117* (1.887)

FXR{2} 0.013 (0.361) FXR{2} -0.048 (0.696)

Covariance and transition probabilities

COV(1,1) 0.786*** (17.087) COV(1,1) 3.953*** (9.172)

COV(2,1) 0.108*** (4.696) COV(2,1) 1.178*** (4.566)

COV(2,2) 0.451*** (14.548) COV(2,2) 3.643*** (8.907)

P(1,1) 0.980*** (163.333) P(1,2) 0.065*** (0.021)

P(2,1) 0.020*** (3.333) P(2,2) 0.935*** (0.021)

43

Panel B. Canada





STR{1} -0.040 (1.081) STR{1} -0.263*** (3.507)

STR{2} -0.040 (1.111) STR{2} -0.126 (1.615)

STR{3} -0.096*** (2.667) STR{3} 0.080 (1.000)

STR{4} -0.060* (1.714) STR{4} 0.095 (1.234)

FXR{1} 0.092* (1.673) FXR{1} 0.533*** (3.211)

FXR{2} 0.028 (0.538) FXR{2} 0.089 (0.527)

FXR{3} 0.013 (0.241) FXR{3} -0.036 (0.208)

FXR{4} 0.075 (1.389) FXR{4} 0.049 (0.277)


Constant 0.042** (2.211) Constant -0.078 (0.987)

STR{1} 0.031 (1.292) STR{1} -0.032 (0.914)

STR{2} 0.006 (0.261) STR{2} -0.024 (0.649)

STR{3} -0.010 (0.400) STR{3} 0.057 (1.541)

STR{4} -0.016 (0.696) STR{4} 0.003 (0.083)

FXR{1} -0.087** (2.289) FXR{1} 0.035 (0.443)

FXR{2} -0.015 (0.417) FXR{2} 0.059 (0.747)

FXR{3} -0.001 (0.029) FXR{3} -0.034 (0.420)

FXR{4} 0.000 (0.000) FXR{4} 0.117 (1.393)


COV(1,1) 0.730*** (15.532) COV(1,1) 6.771*** (8.759)

COV(2,1) 0.193*** (8.773) COV(2,1) 1.705*** (7.016)

COV(2,2) 0.327*** (15.571) COV(2,2) 1.452*** (10.225)

P(1,1) 0.978*** (139.714) P(1,2) 0.080*** (3.333)

P(2,1) 0.022*** (3.143) P(2,2) 0.920*** (38.333)

44

Panel C. Japan





STR{1} -0.107*** (3.057) STR{1} -0.279*** (3.77)

STR{2} -0.044 (1.333) STR{2} -0.168** (2.182)

STR{3} 0.004 (0.118) STR{3} -0.030 (0.385)

STR{4} -0.045 (1.364) STR{4} 0.128* (1.753)

FXR{1} -0.403*** (6.948) FXR{1} -0.719*** (7.049)

FXR{2} -0.111** (1.982) FXR{2} -0.240** (2.051)

FXR{3} -0.026 (0.5) FXR{3} 0.047 (0.398)

FXR{4} -0.095* (1.792) FXR{4} 0.103 (0.873)


Constant -0.015 (0.625) Constant 0.254** (2.032)

STR{1} 0.035* (1.667) STR{1} 0.091* (1.655)

STR{2} 0.005 (0.238) STR{2} 0.099* (1.737)

STR{3} -0.001 (0.048) STR{3} 0.018 (0.31)

STR{4} 0.025 (1.25) STR{4} 0.014 (0.259)

FXR{1} -0.040 (1.081) FXR{1} 0.137* (1.851)

FXR{2} -0.002 (0.056) FXR{2} 0.142 (1.632)

FXR{3} -0.017 (0.515) FXR{3} -0.102 (1.159)

FXR{4} 0.010 (0.303) FXR{4} -0.010 (0.112)


COV(1,1) 1.206*** (16.297) COV(1,1) 6.253*** (8.709)

COV(2,1) -0.155*** (5.536) COV(2,1) -2.148*** (5.698)

COV(2,2) 0.453*** (14.156) COV(2,2) 3.427*** (8.278)

P(1,1) 0.971*** (121.375) P(1,2) 0.110*** (3.929)

P(2,1) 0.029*** (3.625) P(2,2) 0.890*** (31.786)

45

Panel D. Switzerland




Constant 0.084*** (2.897) Constant -0.318** (2.446)

STR{1} -0.004 (0.118) STR{1} -0.033 (0.569)

STR{2} -0.038 (1.118) STR{2} -0.144** (2.441)

STR{3} -0.037 (1.057) STR{3} -0.064 (1.049)

STR{4} -0.036 (1.091) STR{4} 0.106* (1.797)

FXR{1} -0.023 (0.46) FXR{1} -0.310** (2.214)

FXR{2} 0.017 (0.362) FXR{2} 0.091 (0.641)

FXR{3} -0.056 (1.217) FXR{3} 0.159 (1.053)

FXR{4} -0.001 (0.022) FXR{4} 0.447*** (3.000)


Constant 0.040** (2.105) Constant -0.024 (0.4)

STR{1} -0.006 (0.25) STR{1} 0.008 (0.296)

STR{2} 0.070*** (2.917) STR{2} -0.033 (1.179)

STR{3} -0.063*** (2.864) STR{3} -0.025 (0.926)

STR{4} -0.014 (0.583) STR{4} -0.011 (0.393)

FXR{1} -0.071** (2.152) FXR{1} -0.009 (0.145)

FXR{2} -0.057 (1.541) FXR{2} 0.059 (0.797)

FXR{3} -0.017 (0.515) FXR{3} -0.037 (0.544)

FXR{4} 0.003 (0.097) FXR{4} -0.016 (0.235)


COV(1,1) 0.644*** (14.636) COV(1,1) 4.626*** (10.538)

COV(2,1) -0.028 (1.556) COV(2,1) -0.012 (0.094)

COV(2,2) 0.327*** (19.235) COV(2,2) 0.981*** (10.9)

P(1,1) 0.973*** (121.625) P(1,2) 0.081*** (3.375)

P(2,1) 0.027*** (3.375) P(2,2) 0.919*** (38.292)

46

Panel E. United Kingdom




Constant 0.062* (1.879) Constant -0.245 (1.361)

STR{1} -0.052 (1.625) STR{1} -0.120* (1.714)

STR{2} 0.005 (0.152) STR{2} -0.111 (1.563)

STR{3} -0.021 (0.636) STR{3} -0.151** (2.068)

STR{4} -0.049 (1.581) STR{4} 0.228*** (3.123)

FXR{1} -0.102* (1.729) FXR{1} 0.266* (1.652)

FXR{2} -0.006 (0.103) FXR{2} -0.130 (0.788)

FXR{3} -0.069 (1.190) FXR{3} 0.259 (1.551)

FXR{4} 0.070 (1.148) FXR{4} -0.174 (1.048)



STR{1} 0.008 (0.444) STR{1} -0.017 (0.531)

STR{2} 0.031* (1.722) STR{2} -0.034 (1.030)

STR{3} -0.013 (0.765) STR{3} 0.022 (0.667)

STR{4} -0.032* (1.882) STR{4} 0.022 (0.667)

FXR{1} -0.042 (1.273) FXR{1} 0.132* (1.784)

FXR{2} 0.023 (0.719) FXR{2} -0.056 (0.737)

FXR{3} 0.032 (1.032) FXR{3} -0.052 (0.675)

FXR{4} -0.007 (0.212) FXR{4} -0.030 (0.395)


COV(1,1) 0.956*** (14.938) COV(1,1) 6.631*** (8.771)

COV(2,1) 0.062*** (3.444) COV(2,1) 0.989*** (4.281)

COV(2,2) 0.290*** (19.333) COV(2,2) 1.368*** (8.883)

P(1,1) 0.984*** (164.000) P(1,2) 0.067*** (2.913)

P(2,1) 0.016*** (2.667) P(2,2) 0.933*** (40.565)

47

Panel F. Unites States





STR{1} -0.042 (1.200) STR{1} -0.202*** (3.424)

STR{2} -0.058 (1.611) STR{2} -0.134** (2.233)

STR{3} 0.025 (0.694) STR{3} -0.030 (0.492)

FXR{1} -0.064 (1.032) FXR{1} -0.161 (1.052)

FXR{2} -0.101* (1.772) FXR{2} 0.109 (0.699)

FXR{3} 0.065 (1.161) FXR{3} -0.468*** (2.889)


Constant -0.025 (1.471) Constant 0.055 (0.965)

STR{1} -0.025 (1.136) STR{1} 0.003 (0.130)

STR{2} -0.042** (2.000) STR{2} 0.041* (1.708)

STR{3} 0.011 (0.524) STR{3} 0.021 (0.875)

FXR{1} -0.056 (1.556) FXR{1} 0.050 (0.820)

FXR{2} -0.011 (0.324) FXR{2} -0.012 (0.194)

FXR{3} -0.021 (0.618) FXR{3} 0.043 (0.672)


COV(1,1) 0.635*** (7.299) COV(1,1) 6.432*** (9.162)

COV(2,1) -0.098*** (5.158) COV(2,1) -0.934*** (5.627)

COV(2,2) 0.255*** (15.938) COV(2,2) 1.018*** (9.695)

P(1,1) 0.963*** (68.786) P(1,2) 0.091*** (3.138)

P(2,1) 0.037*** (2.643) P(2,2) 0.909*** (31.345)

48

TABLE 9

Estimation Results of Smoothed Probabilities with GARCH Volatilities

Table 9 reports the least square estimation with a heteroscedasticity-robust covariance matrix between smoothed probabilities of high volatility regime and GARCH volatilities. ( )il smp signifies the logistic transformation of the smoothed probabilities. ,S th and ,E th represent the GARCH volatilities of stock market returns and FX market returns. t-statistics are in parentheses. ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively. Variable Australia Canada Japan Switzerland UK US

( )il smp

Constant -4.065*** -4.331*** -5.443*** -3.206*** -5.116*** -3.321***

(-49.125) (-62.361) (-63.526) (-48.242) (-78.088) (-50.911)

Log( ,S th ) 5.046*** 4.115*** 4.174*** 4.08*** 3.907*** 3.522***

(26.587) (32.274) (26.99) (30.505) (38.552) (40.597)

Adj. R-sq 0.484 0.579 0.419 0.572 0.553 0.615

( )il smp

Constant -2.263*** -0.221 -2.501*** 0.022 0.122 1.014***

(-20.456) (-1.266) (-27.718) (0.126) (0.709) (5.532)

Log( ,E th ) 4.029*** 4.295*** 2.79*** 3.498*** 4.366*** 3.672***

(33.446) (31.475) (31.239) (22.714) (30.186) (25.951)

Adj. R-sq 0.461 0.412 0.454 0.268 0.443 0.363

49

TABLE 10

The Summary of Markov-Switching Granger Causality Results

Table 10 reports the summary results of Markov-Switching Granger causality for 6 advanced countries in Table 9. ‘O’ implies the existence of Granger causality and ‘X’ implies no Granger causality, when statistical inferences of Granger causality is based on the Bonferroni and the Scheffe procedures (Savin (1980)). The sub-sample Granger causality tests are the estimation results from the darkened area in Table 7. The critical values for the Bonferroni and the Scheffe procedures are provided for each significance level, according to the optimal lag structure of each countries; Australia shows AR(2) process, U.S. shows AR(3), and other countries show AR(4). The largest t-statistics are in parentheses. ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively, based on the Bonferroni procedure, which has higher power than the Scheffe procedure.

MS Granger Causality Tests Sub-sample Granger Causality Tests

Country Causality Low Variance Period High Variance Period Mid-Crisis

Australia E-/->S O (9.320)*** O (7.231)*** O

S-/->E X (1.077) X (0.814) X

Canada E-/->S X (1.673) O (3.211)*** O

S-/->E X (1.292) X (1.514) X

Japan E-/->S O (6.948)*** O (7.049)*** O

S-/->E X (1.667) X (1.737) X

Switzerland E-/->S X (1.217) O (3.000)** O

S-/->E O (2.864)** X (1.179) X

UK E-/->S X (1.729) X (1.652) X

S-/->E X (1.882) X (1.030) X

US E-/->S X (1.772) O (2.889)** X

S-/->E X (2.000) X (1.708) X

Total E-/->S 2 5 4 S-/->E 1 0 0

Critical Value

Significance Level AR(2) AR(3) AR(4)

B procedure

10% 1.960 2.128 2.241

5% 2.241 2.394 2.498

1% 2.807 2.935 3.023

S procedure

10% 2.148 2.504 2.793

5% 2.451 2.800 3.086

1% 3.042 3.377 3.654

50

TABLE 11

Estimation Results of DCC with Time Dummy Variables

The panel A shows the estimation results of mean equations ( 0 1 1 1, ,1

nTDMt t k t t

kρ γ γ ρ τ ερ= + + +∑−

=), and the panel B presents the estimation results of variance equations

( 2, , 1 2, ,, 1

1

nh c h TDMt t k t tt

kαε β τ υρ ρ ρρ= + + + +∑−−

=). LR test examines the joint significance of time dummy variables in mean equations, variance equation, and both equations.

t-statistics are in parentheses. ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively. Panel A. Mean equations


Constant 0.001*** 0.011*** -0.001 -0.206*** 2814*** -0.001 (4.074) (4.623) (-0.424) (-190.393) (5.07E+05) (-1.403)

RHO{1} 0.993*** 0.967*** 0.969*** 0.726*** 0.989*** 0.988*** (609.586) (154.275) (164.941) (176.908) (3.21E+08) (239.011)

DM1 -2.5E-05 -0.009*** -0.01*** -0.133*** -- 0.003** (-0.184) (-3.55) (-4.241) (-38.971) (2.311)

DM2 4.82E-05 0.008*** -0.017*** 0.057*** 0.276*** -0.009*** (0.358) (4.674) (-4.387) (25.628) (3.637) (-2.979)

DM3 1.9E-04*** 0.013*** -0.009*** 0.133*** 0.267*** -0.005***

(5.225) (4.831) (-3.839) (41.137) (16.520) (-2.922)

DM4 -- 0.004** -0.011*** -- -- -- (2.178) (-3.956)

51

Panel B. Variance equations Australia Canada Japan Switzerland UK US

C 6.45E-09*** 6.97E-05*** 2.44E-04*** 0.001*** 0.003*** 1.70E-04***

(6.246) (4.938) (7.547) (37.692) (11.692) (7.073)

A 0.413*** 0.105*** 0.226*** 0.609*** 0.283*** 0.143*** (9.282) (5.534) (6.516) (12.030) (45.127) (3.923)

B 0.626*** 0.779*** 0.222*** 0.265*** 0.760*** 0.044 (25.459) (22.585) (3.251) (14.242) (237) (0.380)

DM1 2.43E-07** 2.06E-05 5.03E-05* 7.73E-05 0.094*** 1.19E-04***

(2.544) (0.937) (1.672) (0.467) (6.421) (3.576)

DM2 9.34E-08 -5.3E-05*** -9.4E-05** -2.76E-04*** 0.008*** 0.001*** (1.352) (-4.607) (-2.132) (-8.241) (9.543) (4.517)

DM3 -2E-10 -5.1E-05*** -1E-05 2.14E-04** -9.6E-05*** (-0.180) (-4.232) (-0.366) (2.075) (-5.925)

DM4 -5.6E-05*** -8.7E-05*** (-4.551) (-3.408)

Log Likelihood 8804.93 3433.032 3269.552 1813.813 -683.501 3743.646 Panel C. LR Test


0 1,1

: 0n

kk

H τ=

=∑ 27.92*** 42.77*** 20.40*** 3927*** 143.08*** 19.97***

0 2,1

: 0n

kk

H τ=

=∑ 7.36* 24.35*** 68.00*** 69.25*** 66.16*** 49.98***

0 1, 2,1 1

: 0n n

k kk k

H τ τ= =

= =∑ ∑ 35.53*** 65.12*** 89.46*** 3986*** 104.62*** 67.68***

52

TABLE 12

Unit Root and Cointegration Tests for DCCX The panel A reports Zt-bar statistics of Im et al. (2003) for TED, CDS, and ( ),i tl ρ , and ADF-statistics for VIXUS and FXVUS. The panel B presents the result of Pedroni test of panel cointegration (Pedroni, 2004). ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively. Panel A. Unit Root Test Variable Test Statistics VIXUS -1.324 FXVUS -1.226 TED 0.347 CDS 0.396 ( ),i tl ρ 2.820

Panel B. Panel Cointegration Test Statistics Group Rho-statistics 2.527** Group PP-statistics 4.701*** Group ADF-statistics 4.701***

53

TABLE 13

Estimation Results from the DCCX Model

The table presents the result of the DCCX model with random effect. VIX is the volatility index for S&P 500 index options. ( ),i tl ρ signifies the logistic transformation of the DCCs in the absolute value. FXV is the 3 month implied FX volatility index for USD/EUR, TED is the interest rate of each country less LIBOR in 3 month, and CDS is the CDS spread of each country. ‘***’, ‘**’, and ‘*’ represent the significance level of 1%, 5%, and 10%, respectively.

Dependent Variable ( ),i tl ρ

Coefficient t-Statistics Constant -1.550*** (-5.141) VIX{1} 0.029*** (12.141) FXV{1} -0.004 (-0.508) TED{1} 0.120*** (10.616) CDS{1} -0.004*** (-5.105) Number of Observations 2776

54

FIGURE 1

Daily Dollar Exchange Rate and Returns of Major Developed Countries

Figure 1 shows exchange rates and their changes for 6 OECD countries.

Daily USD/AUD Exchange Rate

2006 2007 2008 2009 20100.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05Daily USD/CAD Exchange Rate

2006 2007 2008 2009 20100.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

Daily Returns on USD/AUD Exchange Rate

2006 2007 2008 2009 2010-10

-8

-6

-4

-2

0

2

4

6

8Daily Returns on USD/CAD Exchange Rate

2006 2007 2008 2009 2010-4

-3

-2

-1

0

1

2

3

4

Daily USD/JPY Exchange Rate

2006 2007 2008 2009 20100.003

0.004

0.005

0.006

0.007

0.008

0.009Daily USD/CHF Exchange Rate

2006 2007 2008 2009 20100.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

Daily Returns on USD/JPY Exchange Rate

2006 2007 2008 2009 2010-7.5

-5.0

-2.5

0.0

2.5

5.0

7.5Daily Returns on USD/CHF Exchange Rate

2006 2007 2008 2009 2010-3

-2

-1

0

1

2

3

4

5

Daily USD/GBP Exchange Rate

2006 2007 2008 2009 20101.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2Daily EUR/USD Exchange Rate

2006 2007 2008 2009 20100.625

0.650

0.675

0.700

0.725

0.750

0.775

0.800

0.825

0.850

55

Daily Returns on USD/GBP Exchange Rate

2006 2007 2008 2009 2010-4

-3

-2

-1

0

1

2

3

4Daily Returns on EUR/USD Exchange Rate

2006 2007 2008 2009 2010-4

-3

-2

-1

0

1

2

3

56

FIGURE 2

Daily Stock Index and Returns of Major Developed Countries

Figure 2 shows stock market indices and their returns for six OECD countries.

Daily All Ordinaries Index in Australia

2006 2007 2008 2009 20103000

3500

4000

4500

5000

5500

6000

6500

7000Daily S&P TSX Composite Index in Canada

2006 2007 2008 2009 20107000

8000

9000

10000

11000

12000

13000

14000

15000

16000

Daily Returns on All Ordinaries Index in Australia

2006 2007 2008 2009 2010-10

-8

-6

-4

-2

0

2

4

6Daily Returns on S&P TSX Composite Index in Canada

2006 2007 2008 2009 2010-10.0

-7.5

-5.0

-2.5

0.0

2.5

5.0

7.5

10.0

Daily Nikkei 225 Index in Japan

2006 2007 2008 2009 2010600

800

1000

1200

1400

1600

1800

2000Daily Swiss Market Index in Switzerland

2006 2007 2008 2009 20104000

5000

6000

7000

8000

9000

10000

Daily Returns on Nikkei 225 Index in Japan

2006 2007 2008 2009 2010-15

-10

-5

0

5

10

15Daily Returns on Swiss Market Index in Switzerland

2006 2007 2008 2009 2010-10.0

-7.5

-5.0

-2.5

0.0

2.5

5.0

7.5

10.0

12.5

Daily FTSE 100 Index in UK

2006 2007 2008 2009 20103500

4000

4500

5000

5500

6000

6500

7000Daily S&P 500 Index in US

2006 2007 2008 2009 2010600

800

1000

1200

1400

1600

Daily Returns on FTSE 100 Index in UK

2006 2007 2008 2009 2010-10.0

-7.5

-5.0

-2.5

0.0

2.5

5.0

7.5

10.0Daily Returns on S&P 500 Index in US

2006 2007 2008 2009 2010-10.0

-7.5

-5.0

-2.5

0.0

2.5

5.0

7.5

10.0

12.5

57

FIGURE 3

DCC of Stock Market and FX Market in Major Developed Countries

Figure 3 shows DCCs between exchange rate changes and stock returns estimated by DCC-MGARCH model for 6 OECD countries and structural breaks are shown as vertical lines. Shaded area is contagion period caused by US financial crisis.

59

FIGURE 4

Smoothed Probability of High Variance and GARCH Volatilities

Figure 4 shows smoothed probabilities of the high-variance regime and two broken lines are volatilities of stock returns and exchange rate changes

estimated by MGARCH variance equations in table 4.

Graph A. Australia and Canada

MCMC Probability and GARCH Volatility in AT

PROB_REGIME2 ST_VOLATILITY FX_VOLATILITY

2006 2007 2008 2009 20100.00

0.25

0.50

0.75

1.00

-2

-1

0

1

2

3

4

5

60

Graph B. Japan and Switzerland

MCMC Probability and GARCH Volatility in CN


2006 2007 2008 2009 20100.00

0.25

0.50

0.75

1.00

-2

-1

0

1

2

3

4

MCMC Probability and GARCH Volatility in JP


2006 2007 2008 2009 20100.00

0.25

0.50

0.75

1.00

-3

-2

-1

0

1

2

3

4

5

61

MCMC Probability and GARCH Volatility in SW


2006 2007 2008 2009 20100.0

0.2

0.4

0.6

0.8

1.0

-3

-2

-1

0

1

2

3

4

5

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Graph C. United Kingdom and United States

MCMC Probability and GARCH Volatility in UK


2006 2007 2008 2009 20100.00

0.25

0.50

0.75

1.00

-3

-2

-1

0

1

2

3

4

5

MCMC Probability and GARCH Volatility in US


2006 2007 2008 2009 20100.00

0.25

0.50

0.75

1.00

-3

-2

-1

0

1

2

3

4

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Data Appendix

Country Item Description Source

Australia

Stock Index All Ordinaries Index Datastream Exchange Rate USD/AUD Exchange Rate Datastream Interest Rate Australian Deposit 3-Month Bloomberg CDS Spread Australia CDS USD 5-Year Bloomberg

Canada

Stock Index S&P TSX Composite Index Datastream Exchange Rate USD/CAD Exchange Rate Datastream Interest Rate Canada T-Bill 3Month Datastream CDS Spread Not available Bloomberg

Japan

Stock Index Nikkei 225 Index Datastream Exchange Rate USD/JPY Exchange Rate Datastream Interest Rate Japan T-Bill 3-Month Bloomberg CDS Spread Japan CDS USD 5-Year Bloomberg

Switzerland

Stock Index Swiss Market Index Datastream Exchange Rate USD/CHF Exchange Rate Datastream Interest Rate Swiss Interbank 3-Month Datastream CDS Spread Swiss CDS USD 5-Year Bloomberg

UK

Stock Index FTSE 100 Index Datastream Exchange Rate USD/GBP Exchange Rate Datastream Interest Rate UK T-Bill 3 Month Bloomberg LIBOR GBP LIBOR 3-Month Bloomberg CDS Spread UK CDS USD 5-Year Bloomberg

US

Stock Index S&P 500 Index Datastream Exchange Rate EUR/USD Exchange Rate Datastream Interest Rate T-Bill 3-Month Bloomberg CDS Spread US CDS EUR 5-Year Bloomberg Stock Volatility Index CBOE VIX Index Bloomberg FX Volatility Index USD/EUR 3-Month VIX Datastream

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